2D ANIMATION & INTERACTION COURSE WEEK 5 QUICK REFERENCE

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1 The Imaginary Institute institute.com institute.com 2D ANIMATION & INTERACTION COURSE WEEK 5 QUICK REFERENCE RANDOM NUMBERS By using random numbers, you can generate lots of different objects that all appear to belong to the same family. ou can also add unpredictability to your program. Crea%ng random numbers ou can create a random number within any range by handing the low and high values to random(): // get a value of 5 or more but never quite 10 v = random(5, 10); ou ll get back a value that could be as small as the first number, but never quite as large as the second one. The first number must always be smaller (that is, to the left on the number line) than the second number. If you want to generate the same sequence of random numbers each time you run your program, call randomseed() at the very beginning, giving it any integer you like. // always produce the same random numbers randomseed(10); ARRAS An array can hold a list of any one type of object. To create an array, you first declare it to be a list of that type by naming the type followed by square brackets: float[] berryweights; // declare an array of floats Then you have to actually create the memory for the array by assigning it the result of the keyword new followed by the type, and the desired length of the array in square brackets: berryweights = new float[3]; // the array has 3 entries Then fill in the values of the array one by one by assigning to each entry. To reference a particular element of an array, name the array, followed by an open square bracket, the index, and a closing square bracket, all without spaces. The Imaginary Institute, All rights reserved.

2 Important note: Array index values start at 0. Thus an array of 10 elements will have indices 0 through 9. Asking for an index that is negative, or beyond the length of the array, will cause your program to crash. berryweights[0] = 3.3; berryweights[1] = 2.78; berryweights[2] = 1.5; The length of every array can be found by naming the array followed by a period and the word length. ou can use this to write a loop to fill up an array: for (int i=0; i<berryweights.length; i++) { } berryweights[i] = 3*(i+1); // berries get heavier A shortcut that works only when you re declaring an array is to provide its starting values in curly braces. Processing will count them up for you and automatically allocate the appropriate amount of memory. float berryweights = { 3.3, 2.78, 1.5 }; Array Opera)ons ou can modify an array with built- in operations. In the following, the variable a is the name of the array being manipulated, and b is some other array of the same type. The variables m and n are integers. These all create and return a new array. In all operations that use two arrays, they must both be of the same type (e.g., int or float). append(a, v) arraycopy(a, b) concat(a, b) expand(a, m); reverse(a) shorten(a) sort(a) splice(a,b,n) subset(a,m,n) extend the array by one element and put v in it copy one array to another append one copy to another extend the array by m entries reverse the entries in the array make the array shorter by deleting the last entry sort the entry elements paste array b into array a starting at n extract n entries from a starting at index m Page 2

3 MODULO The modulo operator, written with %, takes two values a and b. When both values are positive, the result of a%b is what s left over when b is subtracted from a as many times as possible without a becoming negative. 8%3 has the value 2, because we remove 3 twice, leaving 2 7%7 has the value 0, as does 14%7, 21%7, etc. Modulo is very useful when working with arrays to make sure we don t go beyond the bounds of the array. For example, if we want to print 100 numbers but our array is less than 100 entries long, we can use modulo to re- use the array entries as many times as needed: for (int i=0; i<100; i++) { int j = i % myarray.length; // j is now between 0 and myarray.length-1 println( entry number +i+ is +myarray[j]); } TRANSFORMS Every reference to a point on the screen has an x and y value. These are always interpreted with respect to the current coordinate system. If we change the coordinate system, then everything we draw after that change will be with respect to the new system. Transformations accumulate. So to make a complex drawing, we often make some transformations, draw some graphics, transform some more, draw more graphics, and so on. Just as when we change drawing specifications like the fill or stroke color, objects already drawn are not affected in any way; only the objects that come after the change depend on the new values. Each time draw() begins, the coordinate system is reset to the default: (0,0) is in the upper left of the graphics window, the X axis points right, the axis points down, and both axes are 1 pixel long. Page 3

4 Translate We can move the origin of the coordinate system with translate(). It tells us how to move along X and to locate the point where the origin ought to go. Note that as always, these x and y values are interpreted with respect to the current coordinate system. translate(tx, ty); // move the origin to (tx,ty) before after Rotate We can re- direct the axes of the coordinate system with rotate(). It takes an angle (in radians), and rotates the coordinate system clockwise by that amount. rotate(angle); // rotate the axes by angle (0,0) X before after Page 4

5 Scale We can change the size of the axes. To multiply the length of both axes by the same amount, hand that value to scale(). A value greater than 1 causes the axes to enlarge, which has the effect of making everything that is then drawn appear larger. A value between 0 and 1 makes the axes shrink, making following objects appear smaller. scale(s); // make everything bigger or smaller by s (0,0) X before after ou can scale each axis by a different amount by using two arguments. This is particularly useful when you want to flip something around one of the axes. For example, to flip an object left to right, but leave it unchanged vertically, scale the X axis by - 1 and the axis by 1. scale(-1, 1); // flip the X axis Important note: If you use the two- argument form of scale and then later rotate the system, you may find that your objects seem to lean, or skew, in some unexpected way. This is a natural result of the mathematics. If you don t want to see skew, then always scale both axes by the same amount by using the one- argument form of scale(). Page 5

6 THE TRANSFORM STACK The system maintains a stack of transformations. Each transformation is represented internally by a mathematical object called a matrix, so this stack is often called the transformation matrix stack, or the matrix stack, or the transform stack. The stack offers a specialized kind of save- and- undo mechanism. To save the current transformation so that you can return to it later, you push it onto the top of the stack. This creates a copy of the current transformation matrix and saves that copy on the top of the stack. ou can continue to make more transformations and push them onto the stack. When you want to undo the most recent set of transformations, you pop the stack. The matrix that s on top is thrown away, and the transformation you saved most recently becomes the active one. pushmatrix(); popmatrix(); // save the current transformation // undo all transforms back to the last push Every push must be followed, eventually, by exactly one pop. Avoid popping more times than you ve pushed. If you ever do try to pop the stack when there s nothing remaining to be popped, your program will crash. Page 6